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If you multiply a number with only 1s by itself, you end up with a palindrome of the numbers in ascending and then descending order. People have called this an example of the “beauty of mathematics.” If your number has N digits of 1, then its square will be the numbers 1 to N in ascending and then descending order. The pattern continues indefinitely, although it “breaks” after 9 because of carry over. I explain why the pattern happens using the method of multiplying by lines.
Multiply by lines: https://www.youtube.com/watch?v=0SZw8jpfAk0
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what if you have more tha 20 ones??
101^0 = 01
101^1 = 0101
101^2 = 010201
101^3 = 01030301
101^4 = 0104060401
101^5 = 010510100501
101^6 = 01061520150601
…
Awesomeeeee!!!
I Can Turn Any Number Into Four Say For Example The Number 20
20 = 6 = 3 = 5 = 4 Because 20 Has 6 Letters In It. Here Count The Letters In Twenty. Repeat This For Every Number It Always Will Equal 4
I've just noticed that your method with the line intersections works not only for squaring but also for multiplying numbers consisting of any count of digit 1. For example 11 * 111 = 1221 , 11 * 1111 = 12221 , 111 * 1111 = 123321 …and so on.
EW COMMON CORE.
Gosh i realised this aswell
i feel nerdz bc i love to watch these videos
Here's another interesting thing. If you know about binomial coefficients, you will instantly be able to calculate 11^4. Why? Because 11^4 = (10+1)^4=14641
Simmilarly 101^8 = 10828567056280801
Which can be calculated by simply looking up in pascal's triangle
if you keep on going as far as the 28th term, the counting pattern actually continues!
123456790 123456790 123456790 098765432 098765432 0987654321
^ ^
all of the sections have all numbers 1-9 except for these. That is because all the sections in the first half have 1-9, and the very last section has 1-9, but all the others don't. This is because we carry over to the left and not the right.
Another way of looking at 111×111:
111×100=11100
111×10= 01110
111×1= 00111
when it is added together it is 12321 (doesn't it look similar to the line thing?)
Here's another way to do it:
1 x 1 =
1
x1
1
And:
111 x 111 =
11100
01110
x 00111
12321
Crap this is intresting. Discovered something simmilar 5 years ago, but forgot that later.
This happens in every base other than decimal too
I always assumed this trick worked because 11 is one more than 10 (the base for our system) but I now see that that is just a coincidence. The reputation of the unit (1) is really what makes this work. Great video!
How about the pattern of the blue numbers in the middle with 10 ones or higher? They go 00, 0120, and is 012340 next?
+MindYourDecisions can you please make a fancy video for the proof of the fundamental theorem of algebra?
Hello mindyourdecisions. i was existed to watch this new video, but i cant watch it. do you know why and how I can fix this? thanks in advance.
It's really amazing. Btw, this lines drawn in 2d, will it work in 3d, with multiply 3 numbers?
I wish we we would switch to base 12. THEN you'd see a lot of fun patterns. And 'decimal' approximations for common ratios would be less necessary (there would still be dodecimal approximations when we have weird things but at least thirds would be 'whole' again in common math)
There's another pattern I have found. When you share
9 / 1
98 / 12
987 / 123
9876 / 1234
…
When you keep sharing this you get closer to 8. Can you explain this?